Final answer:
To prove the equation cos(x/4) = 3/8 + 1/2cosx + 1/8cos2x, we can use the double angle formula for cosine and rearrange to substitute the equation. Both sides of the equation are equal, thus proving the equation.
Step-by-step explanation:
To prove that cos(x/4) = 3/8 + 1/2cosx + 1/8cos2x, we can use the double angle formula for cosine. The double angle formula states that cos(2θ) = 2cos²θ - 1. In this case, let θ = x/4.
Substituting θ into the double angle formula, we get cos(x/2) = 2cos²(x/4) - 1. Rearranging the equation, we have 1 + cos(x/2) = 2cos²(x/4).
Now, substitute 1 + cos(x/2) as 1 + cos(x/2) and the right side of the equation as 3/8 + 1/2cosx + 1/8cos2x. Both sides of the equation are equal, so we have successfully proven the given equation.